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Introductory Statistics 8th Edition Prem S. Mann - Solutions

In a group of adults, some own iPads, and others do not. If two adults are randomly selected from this group, how many total outcomes are possible? Draw a tree diagram for this experiment.
Five hundred employees were selected from a city€™s large private companies, and they were asked whether or not they have any retirement benefits provided by their companies. Based on this information, the following two-way classification table was prepared.a. If one employee is selected
A consumer agency randomly selected 1700 flights for two major airlines, A and B. The following table gives the two-way classification of these flights based on airline and arrival time. €œless than 30 minutes late€ includes flights that arrived early or on time.a. If one
A July 21, 2009 (just a reminder that July 21 is National Junk Food Day) survey on www. HuffingtonPost.com asked people to choose their favorite junk food from a list of choices. Of the 8002 people who responded to the survey, 2049 answered chocolate, 345 said sugary candy, 1271 mentioned ice
Of a total of 100 DVDs manufactured on two machines, 20 are defective. Sixty of the total DVDs were manufactured on Machine 1, and 10 of these 60 are defective. Are the events “Machine I” and “defective” independent?
There are 142 people participating in a local 5K road race. Sixty-five of these runners are female. Of the female runners, 19 are participating in their first 5K road race. Of the male runners, 28 are participating in their first 5K road race. Are the events female and participating in their first
Define the following two events for two tosses of a coin: A = at least one head is obtained B = both tails are obtained a. Are A and B mutually exclusive events? Are they independent? Explain why or why not. b. Are A and B complementary events? If yes, first calculate the probability of B and then
Let A be the event that a number less than 3 is obtained if we roll a die once. What is the probability of A? What is the complementary event of A, and what is its probability?
Thirty percent of last year’s graduates from a university received job offers during their last semester in school. What are the two complementary events here and what are their probabilities?
An automated teller machine at a local bank is stocked with $10 and $20 bills. When a customer withdraws $40 from the machine, it dispenses either two $20 bills or four $10 bills. If two customers withdraw $40 each, how many outcomes are possible? Show all these outcomes in a Venn diagram, and draw
Explain the meaning of the intersection of two events. Give one example.
What is meant by the joint probability of two or more events? Give one example.
How is the multiplication rule of probability for two dependent events different from the rule for two independent events?
What is the joint probability of two mutually exclusive events? Give one example.
Find the joint probability of A and B for the following. a. P (A) = .36 and P (B | A) = .87 b. P (B) = .53 and P (A | B) = .22
Find the joint probability of A and B for the following. a. P (A) = .66 and P (B | A) = .91 b. P (B) = .12 and P (A | B) = .07
Given that A and B are two independent events, find their joint probability for the following. a. P (A) = .17 and P (B | A) = .44 b. P (B) = .72 and P (A | B) = .84
Given that A and B are two independent events, find their joint probability for the following. a. P (A) = .29 and P (B | A) = .65 b. P (B) = .03 and P (A | B) = .28
Given that A, B, and C are three independent events, find their joint probability for the following. a. P (A) = .81 and P (B | A) = .36 b. P (B) = .02 and P (A | B) = .05
Given that A, B, and C are three independent events, find their joint probability for the following. a. P (A) = .30 and P (B | A) = .70 b. P (B) = .40 and P (A | B) = .60
A box contains a certain number of computer parts, a few of which are defective. Two parts are selected at random from this box and inspected to determine if they are good or defective. How many total outcomes are possible? Draw a tree diagram for this experiment.
Given that P (A) = .72 and P (A and B) = .38, find P (B | A).
Given that P (B) = .29 and P (A and B) = .24, find P (A | B).
Given that P (A | B) = .44 and P (A and B) = .33, find P (B)
Given that P(B 0 A) = .70 and P(A and B) = .35, find P(A).
Refer to Exercise 4.52, which contains information on a July 21, 2009 www.HuffingtonPost.com survey that asked people to choose their favorite junk food from a list of choices. The following table contains results classified by gender.a. Suppose that one person is selected at random from this
The following table gives a two-way classification of all basketball players at a state university who began their college careers between 2004 and 2008, based on gender and whether or not they graduated.a. If one of these players is selected at random, find the following probabilities.i. P(female
Five hundred employees were selected from a city€™s large private companies and asked whether or not they have any retirement benefits provided by their companies. Based on this information, the following two-way classification table was prepared.a. Suppose one employee is selected at
Two thousand randomly selected adults were asked whether or not they have ever shopped on the Internet. The following table gives a two-way classification of the responses obtained.a. Suppose one adult is selected at random from these 2000 adults. Find the following probabilities.i. P(has never
A consumer agency randomly selected 1700 flights for two major airlines, A and B. The following table gives the two-way classification of these flights based on airline and arrival time. €œless than 30 minutes late€ includes flights that arrived early or on time.a. Suppose one flight is
Refer to Exercise 4.48. A 2010€“2011 poll conducted by Gallup (www.gallup.com/poll/148994/ Emotional-Health-Higher-Among-Older-Americans.aspx) examined the emotional health of a large number of Americans. Among other things, Gallup reported on whether people had Emotional Health Index
In a group of people, some are in favor of a tax increase on rich people to reduce the federal deficit and others are against it. (Assume that there is no other outcome such as “no opinion” and “do not know.”) Three persons are selected at random from this group and their opinions in favor
In a statistics class of 42 students, 28 have volunteered for community service in the past. If two students are selected at random from this class, what is the probability that both of them have volunteered for community service in the past? Draw a tree diagram for this problem.
In a political science class of 35 s, 21 favor abolishing the Electoral College and thus electing the President of the United States by popular vote. If two s are selected at random from this class, what is the probability that both of them favor abolition of the Electoral College? Draw a tree
In a political science class of 35 students, 21 favor abolishing the Electoral College and thus electing the President of the United States by popular vote. If two students are selected at random from this class, what is the probability that both of them favor abolition of the Electoral College?
Forty-seven employees in an office wear eyeglasses. Thirty-one have single-vision correction, and 16 wear bifocals. If two employees are selected at random from this group, what is the probability that both of them wear bifocals? What is the probability that both have single-vision correction?
Of the 35 students in a class, 22 are taking the class because it is a major requirement, and the other 13 are taking it as an elective. If two students are selected at random from this class, what is the probability that the first student is taking the class as an elective and the second is taking
The probability that a student graduating from Suburban State University has student loans to pay off after graduation is .60. If two students are randomly selected from this university, what is the probability that neither of them has student loans to pay off after graduation?
A contractor has submitted bids for two state construction projects. The probability of winning each contract is .25, and it is the same for both contracts. a. What is the probability that he will win both contracts? b. What is the probability that he will win neither contract?
Five percent of all items sold by a mail-order company are returned by customers for a refund. Find the probability that of two items sold during a given hour by this company, a. Both will be returned for a refund b. Neither will be returned for a refund Draw a tree diagram for this problem.
According to the Recording Industry Association of America, only 37% of music files downloaded from Web sites in 2009 was paid for. Suppose that this percentage holds true for such files downloaded this year. Three downloaded music files are selected at random. What is the probability that all
The probability that a farmer is in debt is .80. What is the probability that three randomly selected farmers are all in debt? Assume independence of events.
Draw a tree diagram for three tosses of a coin. List all outcomes for this experiment in a sample space S.
The probability that a student graduating from Suburban State University has student loans to pay off after graduation is .60. The probability that a student graduating from this university has student loans to pay off after graduation and is a male is .24. Find the conditional probability that a
The probability that an employee at a company is a female is .36. The probability that an employee is a female and married is .19. Find the conditional probability that a randomly selected employee from this company is married given that she is a female.
Recent uncertain economic conditions have forced many people to change their spending habits. In a recent telephone poll of 1000 adults, 629 stated that they were cutting back on their daily spending. Suppose that 322 of the 629 people who stated that they were cutting back on their daily spending
Suppose that 20% of all adults in a small town live alone, and 8% of the adults live alone and have at least one pet. What is the probability that a randomly selected adult from this town has at least one pet given that this adult lives alone?
Explain the meaning of the union of two events. Give one example.
How is the addition rule of probability for two mutually exclusive events different from the rule for two mutually nonexclusive events?
Consider the following addition rule to find the probability of the union of two events A and B: P(A or B) = P(A) + P(B) – P(A and B) When and why is the term P(A and B) subtracted from the sum of P(A) and P(B)? Give one example where you might use this formula.
When is the following addition rule used to find the probability of the union of two events A and B? P(A or B) = P(A) + P(B) Give one example where you might use this formula.
Find P(A or B) for the following.a. P(A) = .66, P(B) = .47, and P(A and B) = .33b. P(A) = .84, P(B) = .61, and P(A and B) = .55
Find P(A or B) for the following.a. P(A) = .28, P(B) = .39, and P(A and B) = .08b. P(A) = .41, P(B) = .61, and P(A and B) = .19Given that A and B are two mutually exclusive events, find
Multiple choice questions: 1. The collection of all outcomes for an experiment is called a. A sample space b. The intersection of events c. Joint probability 2. A final outcome of an experiment is called a. A compound event b. A simple event c. A complementary event 3. A compound event includes a.
Lucia graduated this year with an accounting degree from Eastern Connecticut State University. She has received job offers from an accounting firm, an insurance company, and an airline. She cannot decide which of the three job offers she should accept. Suppose she decides to randomly select one of
There are 200 students in a particular graduate program at a state university. Of them, 110 are female and 125 are out-of-state students. Of the 110 females, 70 are out-of-state students. a. Are the events “female” and “out-of-state student” independent? Are they mutually exclusive? Explain
Reconsider Problem 14. If one of these 200 students is selected at random, what is the probability that the selected student is a female or an out-of-state student?
Reconsider Problem 14. If two of these 200 students are selected at random, what is the probability that both of them are out-of-state students?
The probability that an adult has ever experienced a migraine headache is .35. If two adults are randomly selected, what is the probability that neither of them has ever experienced a migraine headache?
A hat contains five green, eight red, and seven blue marbles. Let A be the event that a red marble is drawn if we randomly select one marble out of this hat. What is the probability of A? What is the complementary event of A, and what is its probability?
The probability that a randomly selected student from a college is a female is .55 and the probability that a student works for more than 10 hours per week is .62. If these two events are independent, find the probability that a randomly selected student is a a. Male and works for more than 10
A sample was selected of 506 workers who currently receive two weeks of paid vacation per year. These workers were asked if they were willing to accept a small pay cut to get an additional week of paid vacation a year. The following table shows the responses of these workers.a. If one person is
Explain the meaning of a random variable, a discrete random variable, and a continuous random variable. Give one example each of a discrete random variable and a continuous random variable.
The following table gives the probability distribution of a discrete random variable x.Find the following probabilities.a. P(x = 3)b. P(x < 2)c. P(x > 4)d. P(1 < x < 4)e. Probability that x assumes a value less than 4f. Probability that x assumes a value greater than 2g. Probability
Alison Bender works for an accounting firm. To make sure her work does not contain errors, her manager randomly checks on her work. Alison recently filled out 12 income tax returns for the company’s clients. Unknown to anyone, 2 of these 12 returns have minor errors. Alison’s manager randomly
The student health center at a university treats an average of seven cases of mononucleosis per day during the week of final examinations.a. Using the appropriate formula, find the probability that on a given day during the finals week exactly four cases of mononucleosis will be treated at this
An average of 6.3 robberies occurs per day in a large city.a. Using the Poisson formula, find the probability that on a given day exactly 3 robberies will occur in this city.b. Using the appropriate probabilities table from Appendix C, find the probability that on a given day the number of
An average of 1.4 private airplanes arrives per hour at an airport.a. Find the probability that during a given hour no private airplane will arrive at this airport.b. Let x denote the number of private airplanes that will arrive at this airport during a given hour.Write the probability distribution
A high school boys’ basketball team averages 1.2 technical fouls per game.a. Using the appropriate formula, find the probability that in a given basketball game this team will commit exactly 3 technical fouls.b. Let x denote the number of technical fouls that this team will commit during a given
Scott offers you the following game: You will roll two fair dice. If the sum of the two numbers obtained is 2, 3, 4, 9, 10, 11, or 12, Scott will pay you $20. However, if the sum of the two numbers is 5, 6, 7, or 8, you will pay Scott $20. Scott points out that you have seven winning numbers and
Suppose the owner of a salvage company is considering raising a sunken ship. If successful, the venture will yield a net profit of $10 million. Otherwise, the owner will lose $4 million. Let p denote the probability of success for this venture. Assume the owner is willing to take the risk to go
Two teams, A and B, will play a best-of-seven series, which will end as soon as one of the teams wins four games. Thus, the series may end in four, five, six, or seven games. Assume that each team has n equal chance of winning each game and that all games are independent of one another. Find the
York Steel Corporation produces a special bearing that must meet rigid specifications. When the production process is running properly, 10% of the bearings fail to meet the required specifications. Sometimes problems develop with the production process that cause the rejection rate to exceed 10%.
Residents in an inner-city area are concerned about drug dealers entering their neighborhood. Over the past 14 nights, they have taken turns watching the street from a darkened apartment. Drug deals seem to take place randomly at various times and locations on the street and average about three per
The following table gives the probability distribution of a discrete random variable x.Find the following probabilities.a. P(x = 1)b. P(x < 1)c. P(x > 3)d. P(0 < x < 2)e. Probability that x assumes a value less than 3f. Probability that x assumes a value greater than 3g. Probability
A high school history teacher gives a 50-question multiple-choice examination in which each question has four choices. The scoring includes a penalty for guessing. Each correct answer is worth 1 point, and each wrong answer costs 12 point. For example, if a student answers 35 questions correctly,
A baker who makes fresh cheesecakes daily sells an average of five such cakes per day. How many cheesecakes should he make each day so that the probability of running out and losing one or more sales is less than .10? Assume that the number of cheesecakes sold each day follows a Poisson probability
Suppose that a certain casino has the €œmoney wheel€ game. The money wheel is divided into 50 sections, and the wheel has an equal probability of stopping on each of the 50 sections when it is spun. Twenty-two of the sections on this wheel show a $1 bill, 14 shows a $2 bill, 7 show a $5
A history teacher has given her class a list of seven essay questions to study before the next test. The teacher announced that she will choose four of the seven questions to give on the test, and each student will have to answer three of those four questions. a. In how many ways can the teacher
Consider the following three games. Which one would you be most likely to play? Which one would you be least likely to play? Explain your answer mathematically.Game I: You toss a fair coin once. If a head appears you receive $3, but if a tail appears you have to pay $1.Game II: You buy a single
Brad Henry is a stone products salesman. Let x be the number of contacts he visits on a particular day. The following table gives the probability distribution of x.Let y be the total number of contacts Brad visits on two randomly selected days. Write the probability distribution for y.
The number of calls that come into a small mail-order company follows a Poisson distribution. Currently, these calls are serviced by a single operator. The manager knows from past experience that an additional operator will be needed if the rate of calls exceeds 20 per hour. The manager observes
Many of you probably played the game “Rock, Paper, Scissors” as a child. Consider the following variation of that game. Instead of two players, suppose three players play this game, and let us call these players A, B, and C. Each player selects one of these three items—Rock, Paper, or
Customers arrive at the checkout counter of a supermarket at an average rate of 10 per hour, and these arrivals follow a Poisson distribution. Using each of the following two methods, find the probability that exactly 4 customers will arrive at this checkout counter during a 2-hour period.a. Use
A review of emergency room records at rural Millard Fell more Memorial Hospital was performed to determine the probability distribution of the number of patients entering the emergency room during a 1-hour period. The following table lists this probability distribution.a. Graph the probability
Nathan Cheboygan, a singing gambler from northern Michigan, is famous for his loaded dice. The following table shows the probability distribution for the sum, denoted by x, of the faces on a pair of Nathan€™s dice.a. Draw a bar graph for this probability distribution.b. Determine the
The H2 Hummer limousine has eight tires on it. A fleet of 1300 H2 limos was fit with a batch of tires that mistakenly passed quality testing. The following table lists the frequency distribution of the number of defective tires on the 1300 H2 limos.a. Construct a probability distribution table for
One of the most profitable items at A1€™s Auto Security Shop is the remote starting system. Let x be the number of such systems installed on a given day at this shop. The following table lists the frequency distribution of x for the past 80 days.a. Construct a probability distribution table for
Five percent of all cars manufactured at a large auto company are lemons. Suppose two cars are selected at random from the production line of this company. Let x denote the number of lemons in this sample. Write the probability distribution of x. Draw a tree diagram for this problem.
According to the most recent data from the Insurance Research Council, 16.1% of motorists in the United States were uninsured in 2010 (virginiabeach.injuryboard.com). Suppose that currently 16.1% of motorists in the United States are uninsured. Suppose that two motorists are selected at random. Let
According to a survey, 30% of adults are against using animals for research. Assume that this result holds true for the current population of all adults. Let x be the number of adults who are against using animals for research in a random sample of two adults. Obtain the probability distribution of
According to the Alzheimer’s Association (www.alz.org/documents_custom/2011_Facts_Figures_ Fact_Sheet.pdf), 3.7% of Americans with Alzheimer’s disease were younger than the age of 65 years in 2011 (which means that they were diagnosed with early onset of Alzheimer’s). Suppose that currently
Classify each of the following random variables as discrete or continuous. a. The time left on a parking meter b. The number of bats broken by a major league baseball team in a season c. The number of cars in a parking lot at a given time d. The price of a car e. The number of cars crossing a
In a group of 12 persons, 3 are left-handed. Suppose that 2 persons are randomly selected from this group. Let x denote the number of left-handed persons in this sample. Write the probability distribution of x. You may draw a tree diagram and use it to write the probability distribution.
In a group of 20 athletes, 6 have used performance-enhancing drugs that are illegal. Suppose that 2 athletes are randomly selected from this group. Let x denote the number of athletes in this sample who have used such illegal drugs. Write the probability distribution of x. You may draw a tree
Briefly explain the concept of the mean and standard deviation of a discrete random variable.
Find the mean and standard deviation for each of the following probability distributions.a.x P(x)0…….. .161…….. .272……..
Find the mean and standard deviation for each of the following probability distributions.a.x P(x)3…….. .094…….. .215……..
Let x be the number of errors that appear on a randomly selected page of a book. The following table lists the probability distribution of x.Find the mean and standard deviation of x.
Let x be the number of magazines a person reads every week. Based on a sample survey of adults, the following probability distribution table was prepared.Find the mean and standard deviation of x.

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